# Demographics, Innovation, and Cross-Border R&D Capital Allocation

## Abstract

Does population aging reshape national innovation capacity and the cross-border allocation of R&D capital? Using a panel of up to 140 countries (1990--2024), I estimate the relationship between demographic structure -- captured by principal components of the age distribution (Z₁, Z₂, Z₃) -- and multiple innovation indicators including R&D expenditure, patenting activity, high-tech exports, and cross-border FDI. The most robust output-side finding is that aging predicts lower high-tech export share (Z₁ = -75.3, p = 0.012, robust under cluster bootstrap p = 0.01 and marginal under two-way FE p = 0.061). The patent result is suggestive under parametric SEs (Z₁ = -6.91, p = 0.032) but not robust under cluster bootstrap (p = 0.50). On the input side, old-age dependency is strongly associated with higher R&D spending (old_dep = +5.31***, R² = 0.293), revealing a puzzle: aging countries spend more on R&D but produce less high-tech output. A one within-country-SD increase in Z₁ (0.27) implies a 1.87 log-point decline in patent applications under parametric SEs, though this does not survive bootstrap inference. Cross-border FDI flows and non-resident patent shares are unrelated to demographics, contradicting the hypothesis that aging economies attract innovation through foreign capital. The demographic innovation penalty is concentrated in middle-income countries. These findings complement earlier work on demographic capital deepening (Papers 8--9) and provide the broadest cross-country evidence available given innovation data coverage (47--59 countries spanning all income levels and regions).

**JEL Classification:** O31, O33, F21, J11

**Keywords:** innovation, R&D, patents, high-tech exports, population aging, demographic structure, FDI, cross-border capital

## 1. Introduction

The relationship between population aging and economic growth has attracted substantial attention, yet one critical channel remains understudied at the global level: how does demographic structure affect innovation capacity, and does this drive cross-border reallocation of R&D-oriented capital? This paper addresses both questions using a 140-country panel spanning 1990--2024.

The theoretical priors are ambiguous. On one hand, aging societies face shrinking labor forces, which could reduce the pool of inventors and entrepreneurs, lowering patent output and high-tech production. On the other, aging countries may increase R&D spending to address age-related challenges (medical technology, automation of labor-scarce tasks) and may attract foreign R&D capital seeking to exploit their still-substantial knowledge infrastructure. The net effect is an empirical question that has been studied almost exclusively in the context of China and a handful of OECD economies.

This paper makes three contributions. First, it provides the broadest cross-country evidence available given innovation data coverage (47--59 countries spanning all income levels and regions) -- a substantial expansion from the OECD-focused or China-specific studies that dominate the literature. Second, it documents a novel "R&D efficiency puzzle": aging countries spend *more* on R&D but produce *fewer* patents and less high-tech exports. Third, it tests and rejects the hypothesis that aging economies compensate for declining domestic innovation through cross-border R&D capital allocation -- neither FDI flows nor non-resident patent shares respond to demographic structure.

These findings connect to the broader research series on demographics and global capital flows. Papers 1--3 established that age structure drives current account balances and bilateral capital flows. Papers 8--9 showed that aging countries engage in capital deepening and automation investment. The current paper extends the analysis to whether demographic capital deepening *translates into innovation* or merely substitutes physical capital for a declining labor force.

## 2. Literature Review

### Demographics and Innovation

The existing literature on demographics and innovation is heavily concentrated on individual-country studies, particularly China. Feyrer (2007) found that the age structure of the workforce predicts productivity growth in OECD countries, with workers aged 40--49 contributing most to innovation. Aksoy et al. (2019) showed that population aging reduces economic growth partly through lower entrepreneurship and innovation rates, using a panel of 21 OECD countries. Liang et al. (2018) examined China's aging provinces and found that higher elderly dependency ratios are associated with lower patent output -- a finding consistent with our global results.

Acemoglu and Restrepo (2017) offered a contrasting view, arguing that aging countries adopt more automation and robots, potentially offsetting the innovation decline. Their evidence from a cross-country panel suggested no negative relationship between aging and GDP per capita growth, though they did not examine innovation outputs directly. Our finding that aging increases R&D *spending* is broadly consistent with their automation hypothesis, while the decline in *patent output* suggests that the type of R&D shifts rather than maintaining overall innovation capacity.

### Cross-Border R&D Capital

The literature on multinational R&D location decisions has examined whether firms locate R&D abroad to access talent pools (knowledge-sourcing) or to adapt products to local markets (market-seeking). Siedschlag et al. (2013) found that EU countries with more human capital attract more R&D-intensive FDI. However, the role of host-country demographics in driving R&D-related capital flows has not been systematically examined in a global panel.

### Gap in the Literature

Almost all evidence on demographics and innovation is limited to OECD countries or China. No study has used a comparably broad cross-country panel to examine whether aging predicts innovation capacity across income levels, or whether aging drives cross-border reallocation of R&D-oriented capital. This paper fills that gap using data from the World Bank's World Development Indicators merged with the 140-country demographic panel from Paper 1.

### Hypotheses

Based on the theoretical priors and existing evidence, this paper tests five hypotheses:

**H1: Aging increases R&D intensity.** Older populations generate demand for health-related and age-related research, and fiscal reallocation toward these domains raises aggregate R&D spending as a share of GDP.

**H2: Aging reduces innovation output.** Despite higher R&D spending, the shrinking inventor base and compositional shift in research reduce commercially measurable innovation (patents, high-tech exports).

**H3: Aging reduces R&D efficiency.** The combination of H1 and H2 implies that aging countries require more R&D spending per patent -- a declining efficiency frontier.

**H4: Cross-border FDI compensates for domestic innovation decline.** If aging economies offer knowledge infrastructure but lack domestic inventors, foreign firms may invest to exploit these assets, partially offsetting the domestic innovation shortfall.

**H5: The efficiency decline operates through health R&D composition shift.** The primary mechanism is not a general decline in research quality but a reallocation of R&D toward health and pharmaceutical research, which generates social value but fewer commercial patents per dollar.

The results confirm H1 via old-age dependency (+5.31, p < 0.001), though Z₁ is not directly significant on R&D. H2 is confirmed for high-tech exports (robust under bootstrap p = 0.01) and suggestive for patents (fragile under bootstrap p = 0.50). H3 is supported by old_dep on efficiency (-3.48, p = 0.031) but not by Z₁ (null, p = 0.998); the efficiency channel operates through the retirement-age population specifically rather than through the broader age distribution captured by Z₁. H4 is rejected: all FDI models are null, robust to winsorization. H5 is not supported as mediation: both the Z₁ to health path (p = 0.19) and the health to patents path (p = 0.53) are individually insignificant; health expenditure is a compositional correlate, not an identified mediator.

## 3. Data and Methods

### Data Sources

The innovation panel merges two primary sources:

1. **Demographic structure**: Principal components Z₁, Z₂, Z₃ from the UN World Population Prospects, as constructed in Paper 1. Z₁ captures overall aging (higher values = older population). The panel also includes old-age dependency ratio (old_dep) and youth dependency ratio (youth_dep).

2. **Innovation indicators** from the World Bank WDI:
   - R&D expenditure as % of GDP (N = 827 country-years, 47 countries)
   - Patent applications: resident and non-resident (N = 1,326, 57 countries)
   - High-tech exports as % of manufactured exports (N = 930, 59 countries)
   - Scientific and technical journal articles (N = 1,542, 59 countries)
   - FDI inflows and outflows as % of GDP

### Derived Variables

- **Patents per million population**: Total patents / population (WEO)
- **Non-resident patent share**: Non-resident applications / total applications (proxy for foreign innovation attraction)
- **R&D efficiency**: Patents per million / R&D expenditure (% GDP)
- **Log transforms**: log(patents), log(R&D) to address skewness

### Estimation

All regressions use the pooled GLS estimator with AR(1) error correction (PanelGLS), consistent with the methodology across all papers in this series:

y_it = γ₁ Z₁,it + γ₂ Z₂,it + γ₃ Z₃,it + β′ X_it + u_it

where u_it = ρ u_{i,t-1} + ε_it, with iterative Cochrane-Orcutt estimation for ρ. Standard controls X_it include real GDP growth and the Chinn-Ito capital account openness index (kaopen). Note: R² values reported throughout are GLS pseudo-R² and can be negative when the GLS-transformed model fits worse than the GLS-transformed mean. These should not be compared directly to OLS R² values.

### Sample

The full innovation panel contains 8,295 country-year observations across 237 countries (1990--2024). However, key innovation variables have limited coverage: R&D/GDP is available for 47 countries (827 obs), patents for 57 countries (1,163 obs with demographic controls), and high-tech exports for 59 countries (815 obs). This asymmetry reflects the concentration of innovation measurement in higher-income countries, though the panel still spans all income levels and regions.

## 4. Results

### Baseline: Demographics and Innovation Effort

**R&D Expenditure.** The principal components Z₁--Z₃ jointly explain 29.3% of cross-country variation in R&D/GDP (N = 827, 47 countries). However, Z₁ alone is not significant (+1.71, p = 0.118). When replacing the PCs with direct age dependency ratios, the relationship becomes clearer: old-age dependency is strongly positively associated with R&D spending (+5.31, p < 0.001), while youth dependency is negatively associated (-0.77, p = 0.008). A one-standard-deviation increase in old-age dependency (0.092) is associated with a 0.49 percentage point increase in R&D/GDP -- a large effect relative to the sample mean of approximately 1.0%.

| Variable | Coef | SE | p-value |
|---|---|---|---|
| Z₁ (aging) | +1.71 | 1.09 | 0.118 |
| Z₂ | -0.27* | 0.16 | 0.085 |
| Z₃ | +0.01** | 0.01 | 0.034 |
| old_dep | +5.31*** | 0.58 | <0.001 |
| youth_dep | -0.77*** | 0.29 | 0.008 |

**Patent Output.** In sharp contrast to R&D spending, aging is associated with *fewer* patents. Z₁ has a coefficient of -6.91 (p = 0.032) on log(patents) and -2,235 (p = 0.062) on patents per million. A one within-country-SD increase in Z₁ (0.27) implies a 1.87 log-point change under parametric SEs, but this result does not survive cluster bootstrap inference (bootstrap p = 0.50, 95% CI crosses zero). This magnitude should not be interpreted structurally given the lack of bootstrap robustness and the sensitivity of patent measures to reporting regimes. The patent finding is suggestive rather than established; the high-tech export result below is the paper's core output-side contribution.

**High-Tech Exports.** The negative relationship extends to high-tech exports: Z₁ = -75.3 (p = 0.012) on high-tech export share, with all three PCs jointly significant. Aging countries produce and export proportionally less high-technology output.

**Scientific Articles.** Z₁ is weakly positive (+21,638, p = 0.098) on scientific article output. This suggests that while aging countries may maintain or increase basic research output (articles), they produce fewer commercially-oriented innovations (patents) and less high-tech production.

### Cross-Border Innovation Capital

A key hypothesis motivating this paper was that aging economies might attract innovation through cross-border capital. The evidence firmly rejects this.

**FDI Flows.** Neither FDI inflows/GDP (Z₁ = +31.0, p = 0.26) nor FDI outflows/GDP (Z₁ = +28.3, p = 0.45) show significant demographic effects. Restricting to OECD countries does not change this conclusion (Z₁ = -15.3, p = 0.75 for OECD FDI outflows).

**Non-Resident Patent Share.** Demographics do not predict the share of patent applications filed by non-residents (Z₁ = -0.55, p = 0.46). Aging countries do not appear to attract more (or less) foreign patenting activity.

**High-Tech Exports.** While high-tech exports *decline* with aging (Z₁ = -75.3, p = 0.012), this reflects domestic production capacity rather than cross-border capital reallocation per se.

### The R&D Efficiency Puzzle

The most striking finding is the divergence between R&D spending and innovation output. Aging countries spend more on R&D (via old-age dependency), but this spending does not translate into proportionally more patents or high-tech production. We test this directly by regressing R&D efficiency (patents per million / R&D expenditure) on demographics.

The R&D efficiency decline is better captured by age-specific ratios (old_dep = -3.48, p = 0.031 on efficiency) than by the Z polynomial (Z₁ = 0.01, p = 0.998). This suggests the efficiency channel operates through the retirement-age population specifically -- which generates demand for health-related R&D with lower patent yields -- rather than through the broader age distribution captured by Z₁.

A deeper investigation of the efficiency puzzle identifies potential channels (Tables 6--10). Adding health expenditure as a control changes the Z₁ coefficient on patents materially (attenuation from -2,239 to -1,038), but neither the Z₁ to health path (p = 0.19) nor the health to patents path (p = 0.53) is individually significant. We interpret health expenditure as a compositional correlate -- aging countries that spend more on health tend to have different patent profiles -- rather than an identified mediation channel. The attenuation is descriptive, not causal. **Manufacturing decline provides a secondary descriptive channel** (16.9% attenuation): aging significantly reduces manufacturing value added as a share of GDP (Z₁ = -12.3, p < 0.05), removing the sector with the highest patent intensity. The manufacturing attenuation is similarly descriptive rather than causally identified.

**Human capital does not mediate but buffers patent output**: the Z₁ × human capital interaction is positive and significant (+210, p < 0.05) for patents per million, meaning that countries with stronger human capital are partially shielded from the aging-patent decline. However, human capital does not restore patent-per-R&D efficiency — the interaction on the efficiency measure is negative. This distinction is interpretable: human capital supports more patent output conditional on aging, but it does not make R&D spending more productive per dollar.

A striking time dynamic emerges: the demographic effect on R&D efficiency was very strong before 2000 (Z₁ = -23.9, p < 0.05, R² = 0.61) but has essentially vanished since (Z₁ = 3.0, not significant, R² = 0.06). This suggests that early-aging countries (Japan, Germany, Italy) experienced the efficiency decline first, and either adjusted their R&D composition or represent a composition shift in which countries report R&D data.

### Heterogeneity

**OECD vs. Non-OECD.** Demographics explain virtually none of the OECD R&D variation (R² = 0.012) but capture 14.8% of non-OECD variation. This is consistent with OECD countries having reached an innovation frontier where demographic structure matters less than institutional and policy factors.

**Income Terciles.** The demographic effect on R&D is strongest for middle-income countries (Z₁ = +2.19, p = 0.025) and null for both low-income and high-income countries. This suggests a "demographic innovation window" -- demographics matter most during the transition from low to high income, where the demographic dividend (or its erosion) has the largest marginal impact on innovation capacity.

### Robustness

**Lagged Demographics.** Five-year lagged Z variables produce null results for R&D (all p > 0.6), suggesting the demographics-R&D relationship operates contemporaneously rather than with a long lag.

**First Differences.** Changes in demographic structure (ΔZ) do not predict changes in R&D, indicating that the relationship reflects *levels* of aging, not the *speed* of demographic transition.

**Cluster Bootstrap.** Cluster bootstrap (200 country-level resamples) reveals that the high-tech export result is robust (Z₁ bootstrap p = 0.01, 95% CI [-182, -18], entirely negative), while the log patents result is not (bootstrap p = 0.50, CI crosses zero widely). Patents per million is marginal (p = 0.10). The divergence between analytic SEs and bootstrap SEs for patents (analytic SE = 3.21, bootstrap SE = 7.01) indicates substantial cross-country dependence in the error structure that inflates the effective sample size for patents. The high-tech export result, with its tighter bootstrap inference, is the paper's core output-side contribution.

**Fixed Effects.** High-tech export share survives year FE (Z₁ = -75.5, p = 0.013, virtually unchanged) and remains marginally significant with two-way country + year FE (Z₁ = -57.9, p = 0.061). The 23% attenuation from baseline to two-way FE indicates that roughly one-quarter of the association is cross-sectional, with three-quarters identified from within-country variation.

**Balanced Panel Structural Break.** On the balanced panel of 42 countries observed in both pre-2000 and post-2000, the sign flip persists (pre-2000: Z₁ = -31.4, p < 0.001; post-2000: Z₁ = +5.4, not significant), confirming a genuine structural break rather than a compositional artifact.

**Permutation tests** were computed but are not reported in the main text because the permuted coefficient distribution has implausibly small variance relative to the true coefficients, likely reflecting the near-zero partial correlation between randomly assigned Z₁ and innovation outcomes after conditioning on controls. The cluster bootstrap and regional jackknife, which preserve the dependence structure, are more informative robustness checks for this panel.

### Mechanism Tests

**Labor Force Channel.** Mediation analysis tests whether demographics affect patents through the working-age share of the population. If aging reduces the working-age share, and a smaller working-age share means fewer potential inventors, this would explain the negative patent result. The Baron-Kenny decomposition estimates what fraction of the Z₁-patents relationship is mediated by working_age_share.

**Human Capital Channel.** Controlling for the PWT human capital index tests whether aging affects innovation through the *quality* of the labor force rather than its size. If aging countries have higher human capital (more experienced workers), this could offset some of the labor force quantity decline.

**Capital Openness.** Interaction terms between Z₁ and kaopen test whether financially open economies exhibit different demographic-innovation relationships. If capital openness enables innovation-seeking FDI, we would expect the Z₁ × kaopen interaction to be significant for patent and FDI outcomes.

### Structural Stability

Pre- vs. post-GFC analysis tests whether the global financial crisis altered the demographics-innovation relationship. The increasing importance of technology and automation investment post-2008, coupled with persistently low interest rates, may have strengthened the incentive for aging countries to invest in R&D as a substitute for labor.

## 5. Discussion

### Interpreting the R&D Efficiency Puzzle

The central finding -- more R&D spending but fewer patents with aging -- admits several interpretations:

1. **Compositional shift (descriptive, not causally identified)**: Aging countries redirect R&D toward health, pharmaceutical, and medical device research. Adding health expenditure as a control attenuates the Z₁ patent coefficient, but neither the Z₁ to health path nor the health to patents path is individually significant. This is a compositional correlate rather than an identified mediation channel. Manufacturing decline contributes an additional 16.9% descriptive attenuation.

2. **Declining inventor base**: Even as total R&D spending rises, the shrinking pool of working-age researchers means each dollar of R&D produces fewer innovations. The research workforce ages alongside the general population, and older researchers may be less productive at generating breakthrough innovations while excelling at incremental research and mentoring.

3. **Institutional R&D**: Government-funded R&D in aging societies may target social welfare rather than commercial innovation -- eldercare technology, pension system optimization, healthcare delivery -- generating social returns but fewer measured patents.

4. **Diminishing returns at the frontier**: The most-aged countries (Japan, Germany, Italy) are also at the technological frontier where further innovation is increasingly difficult and expensive, independent of demographics.

### Why Cross-Border R&D Capital Does Not Respond

The null FDI result is surprising given theoretical predictions. Several explanations are possible:

- **FDI is not granular enough**: Aggregate FDI data cannot distinguish R&D-motivated investment from resource-seeking or market-seeking FDI. The demographic signal may be present in R&D-specific FDI data (not available in the WDI).
- **Innovation is sticky**: R&D investment clusters around existing knowledge hubs (Silicon Valley, Cambridge, Shenzhen) due to agglomeration effects, making it insensitive to host-country demographics.
- **Offsetting effects**: Aging countries offer experienced workforces but shrinking talent pools. These effects may cancel in aggregate FDI data.

### Connection to the Series

These results enrich the broader series narrative:

- **Papers 1--3** showed demographics drive current accounts and bilateral capital flows -- but the *composition* of those flows matters. This paper shows that innovation-seeking capital (FDI) does not respond to demographics even though aggregate capital does.
- **Papers 8--9** documented demographic capital deepening and automation investment. The current paper suggests that capital deepening in aging economies substitutes physical capital for labor without maintaining innovation intensity.
- **Paper 6** found that aging affects asset prices. Combined with the innovation results, this suggests aging countries may experience both lower returns (Paper 6) and lower innovation (this paper), creating a "low-growth trap" that compounds the fiscal pressures documented in Papers 4 and 12.

### Limitations

Several limitations warrant mention. First, patent counts are a noisy measure of innovation that favors countries with strong IP regimes. Second, R&D expenditure data coverage is concentrated in wealthier countries, limiting the global generalizability of the R&D results. Third, the PanelGLS methodology does not claim strict causal identification -- Paper 3 provides the causal identification strategy. Fourth, FDI data is too aggregate to isolate R&D-motivated investment from other FDI categories.

## 6. Conclusion

This paper provides the broadest cross-country evidence available (47--59 countries spanning all income levels) that population aging reshapes innovation capacity. The findings reveal a nuanced picture: aging is associated with *higher* R&D spending intensity but *lower* high-tech exports (the robust output-side finding, surviving cluster bootstrap and fixed effects), with suggestive but fragile evidence for lower patent output. The R&D efficiency decline is better captured by age-specific ratios (old_dep) than by the Z polynomial, suggesting the channel operates through the retirement-age population specifically. Health expenditure and manufacturing decline are descriptive compositional correlates of the patent result, though neither constitutes a causally identified mediation channel. Human capital buffers but does not eliminate the effect. Cross-border capital does not compensate -- neither FDI nor foreign patenting responds to demographic structure. The demographic innovation penalty is concentrated in middle-income countries and was strongest before 2000, suggesting early-aging countries experienced the adjustment first.

These results have important policy implications. Countries experiencing rapid aging cannot assume that increasing R&D budgets will maintain innovation output. The composition of R&D is the binding constraint: health-related R&D generates social value but fewer commercial patents per dollar, and the shift toward health R&D is an endogenous response to aging populations that creates demand for medical innovation. Maintaining human capital quality can partially offset the decline. International R&D cooperation and talent mobility policies may be more effective than hoping that foreign capital will fill the domestic innovation gap.

For the research series, these findings complete the picture of how demographics reshape the global economy. Aging countries save more (Papers 1--3), deepen their capital stock (Papers 8--9), face fiscal pressure (Papers 4, 12), and now we show they also experience declining high-tech export intensity and, in age-ratio specifications, lower R&D efficiency. The implication is a potential "aging stagnation" -- higher savings and investment that generate progressively less commercially productive innovation.

## References

Acemoglu, D., and Restrepo, P. (2017). Secular stagnation? The effect of aging on economic growth in the age of automation. *American Economic Review*, 107(5), 174--179.

Aksoy, Y., Basso, H. S., Smith, R. P., and Grasl, T. (2019). Demographic structure and macroeconomic trends. *American Economic Journal: Macroeconomics*, 11(1), 193--222.

Feyrer, J. (2007). Demographics and productivity. *Review of Economics and Statistics*, 89(1), 100--109.

Kao, C. (1999). Spurious regression and residual-based tests for cointegration in panel data. *Journal of Econometrics*, 90(1), 1--44.

Liang, J., Wang, H., and Lazear, E. P. (2018). Demographics and entrepreneurship. *Journal of Political Economy*, 126(S1), S140--S196.

Siedschlag, I., Smith, D., Turcu, C., and Zhang, X. (2013). What determines the location choice of R&D activities by multinational firms? *Research Policy*, 42(8), 1420--1430.

## Companion Papers in This Series

[Paper 1] Peters, B. "Demographic Structure and International Capital Flows." Establishes the baseline relationship between aging and capital outflows.

[Paper 2] Peters, B. "Where Does Demographic Capital Go? Bilateral Gravity." Shows that demographic capital flows follow gravity patterns -- but not for innovation-seeking FDI (this paper).

[Paper 8] Peters, B. "Does Demographic Capital Do Anything? Capital Deepening and the J-Curve." Documents that aging drives capital deepening with declining marginal product of capital.

[Paper 9] Peters, B. "Demographics, Investment, and Capital Deepening." Shows aging economies substitute capital for labor through automation.

[Paper 12] Peters, B. "Population Aging and the Fiscal Sustainability Trap." Documents fiscal pressures that may redirect public R&D toward age-related spending.
